Global stability in chemostat-type plankton models with delayed nutrient recycling
type: Item
instance of: scholarly article
title: Global stability in chemostat-type plankton models with delayed nutrient recycling
zbMATH Open document ID: 0935.92034
author: Shigui Ruan
author: Xue-Zhong He
published in: Journal of Mathematical Biology
publication date: 1998-10-14T00:00:00Z
review text: This paper considers chemostat-type plankton models with delays, and proves global attractivity of the positive equilibrium in the following cases: delays in the nutrient recycling, first of all, a continuous delay, with a fading memory term, then a discrete constant and finally a discrete variable delay; delays in both the nutrient recycling and the growth response. Proofs are done by setting up integral expressions involving the state variables, and finding sufficient conditions in terms of the average time delay under which these expressions are Lyapunov functionals. A thorough introduction presents arguments, gathered from the literature, regarding the type of model considered in the paper (the Monod model is chosen here rather than the Droop model) and also the importance of delay in systems with nutrient recycling. Finally, comparisons are made with the literature, notably with work by E. Beretta and coworkers.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 1211564
zbMATH Keywords: plankton model
zbMATH Keywords: delayed nutrient recycling
zbMATH Keywords: delayed growth response
zbMATH Keywords: infinite delay
zbMATH Keywords: global attractivity
zbMATH Keywords: Lyapunov functionals
reviewed by: Ovide Arino
MaRDI profile type: Publication
full work available at URL: s002850050128
OpenAlex ID: W1967962353
DOI: 10.1007/S002850050128
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description: scientific article; zbMATH DE number 1211564